huangyhg

calculate beam deflection using spreadsheets
i have created a simply supported beam spreadsheet to design wood beams. i have figured out that with the use of superposition i can combine the affects of each load to determine the total affect on the beam. i have used this principle to determine the shear and moment at every 100th of a foot on the beam. now that i know the moment at every point on the beam is there an easy way to calculate the deflection using the moment-area method or conjugate beam method?
i need something that will give the deflection at any point along the beam for any load case.
can i double integrate the moment at each point on the beam to determine the slope and deflection?
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yes
hi bozzo
you can use any of the methods you mention however the method you choose should be one that suits your requirements best ie:- "the moment area method" is useful when you require a slope or deflection at a single point with reference to another point having zero slope.
the direct intergration method is useful when the bending moment equation is valid across the whole length of the beam.
i don't think you will find a single method suited for all loading conditions and you may have to choose a method as stated earlier.
several other methods to mention which i have used in the past are "step functons","macaulay's method","castigliano" and "srain energy"
regards
desertfox

hi bozzo,
you already have the bending moments at every 100th of a foot, so why not continue along the same lines with the method of `virtual work`.
if you are not familiar with this method -
apply a unit load (1.0 with no units) to the the beam at the position where the deflection is required and calculate the `unit bending moments` at every 100th of a foot.
then at each 100th of a foot, multiply the two bending moment values to give a third value (lb.in^2) at each position. calculate the area under the new set of values (lb.in^3) and divide by ei (lb.in^2) to give the deflection (in) at the point of `unit load`. repeat the procedure at each point along the beam to find the deflection at each 100th of a foot.
the formula is simply - deflection = m.m.dx/ei
the calculations are repetitive, but should be easily programmable into a spreadsheet!
regards,
neilmo
thanks everyone, especially neilmo. the sheet is working great.
glad to be of help.
neilmo

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